Abstract
The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.
Highlights
Curved beams are more efficient in transfer of loads than straight beams because the transfer is affected by bending, shear, and membrane action
A new finite element formulation of the circular arch element was presented in this paper using Trigonometric function
Despite other conventional methods which use displacement functions, the element curvature in current study is defined by three nodal curvatures
Summary
Curved beams are more efficient in transfer of loads than straight beams because the transfer is affected by bending, shear, and membrane action. Some of the structures such as arches and arch bridges are modeled using curved beam elements. The finite element analysis of curved beam has been given significant attention by researchers in recent years mostly because it is a versatile method for solving structural and other mechanical problems
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